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Statements

Subject Item
dbr:Disjoint_union_(topology)
rdfs:label
Disjoint union (topology) 直和 (位相空間論)
rdfs:comment
In general topology and related areas of mathematics, the disjoint union (also called the direct sum, free union, free sum, topological sum, or coproduct) of a family of topological spaces is a space formed by equipping the disjoint union of the underlying sets with a natural topology called the disjoint union topology. Roughly speaking, in the disjoint union the given spaces are considered as part of a single new space where each looks as it would alone and they are isolated from each other. 位相空間論および関連した数学の分野において、位相空間の族の非交和（ひこうわ、英: disjoint union）または直和（ちょくわ、英: direct sum）とは、台集合の非交和（集合の直和）に非交和位相 (disjoint union topology) と呼ばれるを入れることによって形成される位相空間を言う。乱暴な言い方をすれば、2つ以上の空間をそれぞれ個々の空間と見なすと同時に、すべて一緒にした一つの空間としても考えるということである。 非交和空間は積空間の構成の圏論的双対となるため、余積 (coproduct) とも呼ばれる。そのほかにも、自由合併 (free union)、自由和 (free sum)、位相和 (topological sum) などの呼び名もある。
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n16:Coproduct-02.png
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dbr:Natural_topology dbr:If_and_only_if dbr:Topological_union dbr:T0_space dbr:Mathematics dbr:Categorical_dual dbr:Continuous_function_(topology) dbc:General_topology dbr:Quotient_topology dbr:Topological_space dbr:Iff dbr:Product_topology dbr:Hausdorff_space dbr:Coproduct dbr:General_topology dbr:Product_space dbr:Final_topology dbr:Open_set dbr:Universal_property dbr:Disjoint_union dbr:Subspace_(topology) dbr:Disconnected_(topology) n18:Coproduct-02.png dbr:Subspace_topology dbr:Discrete_space dbr:T1_space dbr:Indexed_family dbr:Finest_topology dbr:Open_and_closed_maps dbr:Homeomorphic dbr:Preimage dbr:Category_of_topological_spaces dbr:Topological_embedding dbr:Commutative_diagram
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dbo:abstract
In general topology and related areas of mathematics, the disjoint union (also called the direct sum, free union, free sum, topological sum, or coproduct) of a family of topological spaces is a space formed by equipping the disjoint union of the underlying sets with a natural topology called the disjoint union topology. Roughly speaking, in the disjoint union the given spaces are considered as part of a single new space where each looks as it would alone and they are isolated from each other. The name coproduct originates from the fact that the disjoint union is the categorical dual of the product space construction. 位相空間論および関連した数学の分野において、位相空間の族の非交和（ひこうわ、英: disjoint union）または直和（ちょくわ、英: direct sum）とは、台集合の非交和（集合の直和）に非交和位相 (disjoint union topology) と呼ばれるを入れることによって形成される位相空間を言う。乱暴な言い方をすれば、2つ以上の空間をそれぞれ個々の空間と見なすと同時に、すべて一緒にした一つの空間としても考えるということである。 非交和空間は積空間の構成の圏論的双対となるため、余積 (coproduct) とも呼ばれる。そのほかにも、自由合併 (free union)、自由和 (free sum)、位相和 (topological sum) などの呼び名もある。
gold:hypernym
dbr:Space
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wikipedia-en:Disjoint_union_(topology)?oldid=1020228955&ns=0
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3893
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